Given that m and N are positive integers and M + 3N can be divisible by 11, can m + 3N + 5 be divisible by 11?

Because m + 3N + 5 - (M + 3n) = 3N (35-1) = 242 × 3N = 11 × 22 × 3N, M + 3N + 5 = m + 3N + 11 × 22 × 3N. Since m + 3N can be divisible by 11, M + 3N + 11 × 22 × 3N can also be divisible by 11, so m + 3N + 5 can be divisible by 11

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